A metaphysical conceit is like a metaphor on steroids. Every metaphor is an attempt to connect two unlike things by some commonality, but a metaphysical conceit takes that idea to the extreme. The metaphors are crazy. "Our love? Yeah, it's like a dead guy. Or… no, it's like planetary alignment. No, wait, it's like hammering gold. No, I've got it now, it's like that thing you used in math class to draw circles." Nothing screams John Donne like a good conceit, and this poem has some of his best.
This is a love poem—shouldn't we expect some really gushy, romantic nonsense? Shouldn't this read like the back of a seventh-grade girl's notebook? Maybe, but that's not what we get. Much of this poem reads like the closing argument of a trial, which is no surprise for a John Donne poem. Because of the outlandish conceits, Donne is always out to prove something in his poetry, trying to persuade his audience that even though these images sound completely nutty, they actually (weirdly) make sense. This legal-like language, even in a love poem, is totally Donne.